Ideal solutions are similar to ideal-gas mixtures, but they to not follow the ideal-gas law. The internal energy and enthalpy for ideal solutions were introduced in Section 3.5. Since these properties are additive, the partial molar properties are equal to the pure component properties,
As for the entropy change of mixing, the loss of order due to mixing is unavoidable, even for ideal solutions. During our consideration of the microscopic definition of entropy, we derived a general expression for the ideal entropy change of mixing, Eqn. 4.8.
The entropy of mixing is nonzero for an ideal solution.
Although we derived Eqn. 4.8 for mixing ideal gases, it also provides a reasonable approximation for mixing liquids of equal-sized molecules. The reason is that changes in entropy are related to the change in accessible volume. Even though a significant volume is occupied by the molecules themselves in a dense liquid, the void space in one liquid is very similar to the void space in another liquid if the molecules are similar in size and polarity. That means that the accessible volume for each component doubles when we mix equal parts of two equal-sized components. That is essentially the same situation that we had when mixing ideal gases. The partial molar entropy of mixing is
Given the effect of mixing on these two properties, we can derive the effect on other thermodynamic properties, which has the same formula as that found for ideal gases:
The general relationship for ΔGmix gives a relationship for fugacity. We can extend our definition of the enthalpy of mixing to the Gibbs energy of mixing,
But by using Eqns. 10.42 and 10.48,
Thus, comparing Eqns. 10.67 and 10.65, for an ideal solution, 
.
By comparing the relations in the logarithms, we obtain the Lewis-Randall rule for ideal solutions:
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